Towards Fine-Grained Optimal 3D Face Dense Registration: An Iterative Dividing and Diffusing Method

Dense vertex-to-vertex correspondence (i.e. registration) between 3D faces is a fundamental and challenging issue for 3D &2D face analysis. While the sparse landmarks are definite with anatomically ground-truth correspondence, the dense vertex correspondences on most facial regions are unknown. In this view, the current methods commonly result in reasonable but diverse solutions, which deviate from the optimum to the dense registration problem. In this paper, we revisit dense registration by a dimension-degraded problem, i.e. proportional segmentation of a line, and employ an iterative dividing and diffusing method to reach an optimum solution that is robust to different initializations. We formulate a local registration problem for dividing and a linear least-square problem for diffusing, with constraints on fixed features on a 3D facial surface. We further propose a multi-resolution algorithm to accelerate the computational process. The proposed method is linked to a novel local scaling metric, where we illustrate the physical significance as smooth adaptions for local cells of 3D facial shapes. Extensive experiments on public datasets demonstrate the effectiveness of the proposed method in various aspects. Generally, the proposed method leads to not only significantly better representations of 3D facial data, but also coherent local deformations with elegant grid architecture for fine-grained registrations.